1. INTRODUCTION TO NEW THEORY OF FLIGHT REVEALING THE SECRET OF FLIGHT
UNDERSTANDING
WHY IT IS POSSIBLE TO FLY
JOHAN HOFFMAN JOHAN JANSSON CLAES JOHNSON

2. WEB SITE: THE SECRET OF FLIGHT
MATHEMATICS
FLUID MECHANICS
COMPUTATION
MEASUREMENT
APPLICATIONS
HISTORY

3. NEW THEORY SUBMITTED TO AIAA
MAIN JOURNAL OF AERONAUTICS
NOW UNDER SCRUTINY OF EXPERTS
FOLLOW THE REVIEW PROCESS ON WEB SITE
FIRST VERSION PRESENTED IN NORMAT 2009

4. OLD THEORY KUTTA-ZHUKOVSKY 1904 FATHERS OF MODERN AERONAUTICS
PRANDTL 1904
FATHER OF MODERN FLUID MECHANICS
KZP THEORY

5. SCIENTIFIC MATHEMATICAL THEORIES
FOR UNEDUCATED:
1. TRIVIAL AND CORRECT
2. TRIVIAL AND INCORRECT
FOR EDUCATED:
3. NON-TRIVIAL AND INCORRECT: OLD
4. NON-TRIVIAL AND CORRECT: NEW

6. NEW THEORY
PHYSICAL
MATHEMATICAL
CORRECT
DOES REVEAL THE SECRET
USEFUL

7. OLD THEORY UNPHYSICAL UNMATHEMATICAL INCORRECT
DOES NOT REVEAL THE SECRET
DANGEROUS

8. WHAT TO EXPLAIN: LIFT / DRAG =L/D = 10 - 70 AIRBUS L/D=20 GLIDER L/D=70

9. THE SECRET: L/D = 10 - 70 SURPRISING INGENIOUS ELEGANT
INCOMPRESSIBLE FLOW
SLIGHTLY VISCOUS FLOW

10. IS THEORY NEEDED? BIRDS HAVE LEARNED TO FLY WITHOUT THEORY OF FLIGHT
BUT IT TOOK 100 MILLION YEARS
FROM DINOSAUR TO ARCHAEOPETRYX
HUMANS HAVE LEARNED TO FLY WITHOUT
BUT IT TOOK 500 YEARS
FROM DA VINCI TO SUCCESS: GOSSAMER CONDOR 1978
BECAUSE OF LACK OF THEORY!!

11. DA VINCI FLYING MACHINE 1500

12. GOSSAMER CONDOR 1978 FIRST HUMAN POWERED FLIGHT

13. CONFESSIONS ABOUT OLD THEORY

14. NEW YORK TIMES 2003 (CHANG)
To those who fear flying, it is probably disconcerting that physicists and aeronautical engineers still passionately debate the fundamental issue underlying this endeavor: WHAT KEEPS PLANES IN THE AIR?

15. NASA LISTS INCORRECT THEORIES
LONGER DISTANCE
SKIPPING STONE
VENTURI
BUT NO THEORY CLAIMED TO BE CORRECT!!
NASA DOES NOT SEEM TO KNOW WHAT KEEPS PLANES IN THE AIR!!

16. LONGER PATH THEORY INCORRECT

17. SKIPPING STONE THEORY: NEWTON

18. VENTURI THEORY: BERNOULLI

19. HOFFREN 2001 AIAA A SATISFACTORY THEORY OF LIFT IS STILL LACKING
THERE IS A GENUINE NEED FOR ONE

20. WHAT KEEPS PLANES IN THE AIR?
INCORRECT THEORY OK AS LONG AS YOU DON’T USE IT
NOT USEFUL
NEW THEORY: CORRECT: USEFUL

21. WHY CORRECT THEORY ONLY 2009?
COMPUTE TURBULENT SOLUTIONS OF
NAVIER-STOKES EQUATIONS + SLIP BC
DIRECT SIMULATION WITHOUT TURBULENCE MODELING
POSSIBLE WITH ~ 1 MILLION MESH POINTS
COMPUTATION TELLS THE TRUTH
STUDY REVEALS THE SECRET

22. DRAG CAR COMPUTABLE

23. LIFT DRAG WING COMPUTABLE VELOCITY PRESSURE

24. PRESSURE DISTRIBUTION C_P UPPER LOWER SURFACE

25. LIFT DRAG OF WING COMPUTABLE MAX L = 1.5 L/D = 50 AOA = 16

26. TO UNDERSTAND: STABILITY
STABILITY - INSTABILITY OF FLUID MOTION
STABLE COMPUTABLE ASPECTS OF TURBULENT FLOW
LIFT DRAG MOMENTS..: COMPUTABLE
ALL YOU MAY WANT TO KNOW: COMPUTABLE

27. OPPOSING FLOW INSTABILITY

28. STABLE ATTACHMENT UNSTABLE SEPARATION: OPPOSING FLOW

29. FROM CYLINDER TO AIRFOIL: ROUNDED LEADING + TRAILING EDGE UNDERST CYL = UNDERSTAND AIRFOIL

30. SHORT STORY: THEORIES OF FLIGHT
NEWTON 17H MATH: IMPOSSIBLE: WRONG
D’ALEMBERT 18TH MATH: IMPOSSIBLE: WRONG
WRIGHT BROTHERS 1903 REAL EXP : POSSIBLE
KUTTA-ZHUKOVSKY 1904 MATH: POSSIBLE: WRONG: OLD THEORY OF FLIGHT
HOFFMAN-JOHNSON 2009 MATH: POSSIBLE: RIGHT: NEW THEORY OF FLIGHT

31. NEW VS OLD THEORY NEW THEORY REVEALS THE SECRET OF FLIGHT
OLD THEORY HIDES THE SECRET OF FLIGHT
OLD: RULING PARADIGM
OLD: NOT FUNCTIONAL
NEW INCOMPATIBLE WITH OLD
SCIENTIFIC REVOLUTION A LA KUHN

32. LIFT AND DRAG OF LONG WING
SUCTION ON UPPER LEADING EDGE/SURFACE:
LIFT + NEGATIVE DRAG
PUSH ON LOWER LEADING EDGE/SURFACE:
LIFT + POSITIVE DRAG
FLOW SEPARATES AT TRAILING EDGE WITHOUT PRESSURE RISE/DROP: ELEGANT SEPARATION

33. AIRFOIL – AIRPLANE WING

34. OBSERVATION WIND TUNNEL

35. OBSERVATION: 2D SECTION OF 3D

36. OBSERVATION LIFT UPPER LEADING EDGE SUCTION LOWER LEADING EDGE PUSH
DRAG
LEADING EDGE PUSH/SUCTION
SEPARATION WITHOUT PRESSURE RISE/DROP
DOWNWASH

37. RECALL C_P UPPER LOWER

38. NAVIER-STOKES

39. PRESSURE AOA = 5

40. VELOCITY AOA = 10

41. VELOCITY AOA = 10

42. VELOCITY AOA = 15

43. UNDERSTANDING: THEORY
MATHEMATICAL MODEL OF PHYSICS
ASSUMPTIONS
MATHEMATICAL MODEL = EQUATION:
NAVIER-STOKES + BC: GENERAL
LAPLACE + BC: SPECIAL
MATHEMATICAL THEORY: SOLVE EQUATION

44. LAPLACE EQN: POTENTIAL FLOW
INCOMPRESSIBLE: CORRECT FOR SUBSONIC FLIGHT
INVISCID - SMALL VISCOSITY: CORRECT
SLIP BOUNDARY CONDITION: SMALL SKIN FRICTION: CORRECT
IRROTATIONAL?? NO VORTICES
STATIONARY??
2D??
V = GRADIENT OF HARMONIC FUNCTION
2D FOR CYLINDER LONG WING
VALID!! EVERYWHERE!! NAVIER-STOKES
VALID?? SOMEWHERE BUT NOT EVERYWHERE!! LAPLACE??

45. 1- 4 : LAPLACE’S EQN: POTENTIAL: HARMONIC FUNCTION + SLIP

46. LAPLACE VS NAVIER-STOKES
LAPLACE SIMPLIFIED VERSION OF NAVIER-STOKES
POTENTIAL SOLUTION: 2D
STATIONARY
IRROTATIONAL
LAPLACE SOLUTIONS NOT TURBULENT
NAVIER-STOKES SOLUTIONS TURBULENT

47. CIRC CYLINDER: POTENTIAL FLOW: P = 0 P = 1 P = - 3 V = 1 V = 0 V = 2

48. POTENTIAL FLOW: BERNOULLI’S LAW
½ V2 + P = CONSTANT
HIGH PRESSURE P – LOW VELOCITY V
LOW PRESSURE P – HIGH VELOCITY V

49. CIRC CYLINDER: POTENTIAL FLOW: ZERO LIFT + ZERO DRAG (L/D = 3)

50. LIFT OF HALF CYLINDER

51. THEORY: POTENTIAL FLOW: D’ALEMBERT’S PARADOX 1752: ZERO LIFT AND DRAG

52. POTENTIAL FLOW VS OBSERVATION

53. POTENTIAL FLOW SEPARATION BEFORE TRAILING EDGE
HIGH PRESSURE AT SEPARATION REQUIRED TO BRING FLOW TO STAGNATION
NO DOWNWASH
MATHEMATICAL SOLUTION
BUT NOT OBSERVED IN REALITY
UNPHYSICAL!! WHY??

54. WHAT’S WRONG WITH POTENTIAL FLOW??
D’ALEMBERT COULD NOT UNDERSTAND 1752

55. D’ALEMBERT’S PARADOX 1752
It seems to me that the theory (potential flow), developed in all possible rigor, gives, at least in several cases, a strictly vanishing resistance, a singular paradox which I leave to future Geometers to elucidate”.

56. WHAT’S WRONG WITH POTENTIAL FLOW??
EULER COULD NOT UNDERSTAND
???? 18TH
POTENTIAL FLOW SOLVES
EULER’S EQNS

57. WHAT’S WRONG WITH POTENTIAL FLOW??
LAPLACE COULD NOT UNDERSTAND
???? 19TH
POTENTIAL FLOW SOLVES
LAPLACE’S EQN

58. WHAT’S WRONG WITH POTENTIAL FLOW??
CAUCHY COULD NOT UNDERSTAND
???? 19TH
MASTER OF
HARMONIC FCNS

59. WHAT’S WRONG WITH POTENTIAL FLOW??
POISSON COULD NOT UNDERSTAND
??? 19TH
NOBODY COULD
UNDERSTAND

60. WILBUR + ORWILLE WRIGHT: FLYER DEC 17 1903

61. KUTTA-ZHUKOVSKY 1904 SEPARATION AT TRAILING EDGE BY ADDING CIRCULATION
LIFT BUT NO DRAG

62. FATHERS OF MODERN AERODYNAMICS

63. CIRCULATION: LIFT BUT NO DRAG

64. FATHER OF MODERN FLUID MECHANICS

65. LUDWIG PRANDTL 1904 SLIP BOUNDARY CONDITION IS WRONG NO-SLIP IS RIGHT:
THIN BOUNDARY LAYER
DRAG BUT NO LIFT

66. TURBULENT WAKE: DRAG BUT NO LIFT

67. INCORRECT + INCORRECT = CORRECT?
(-1) x (-1) = 1
NO!!
PRANDTL INCORRECT
KUTTA-ZHUKOVSKY INCORRECT
WHAT IS THEN CORRECT?

68. RESOLUTION OF D’ALEMBERT’S PARADOX
JOHAN HOFFMAN AND CLAES JOHNSON
J MATHEMATICAL FLUID MECHANICS 2008
FINALLY AFTER 256 YEARS
SPIN-OFF: SECRET OF FLIGHT 2012

69. POTENTIAL FLOW: STABLE ATTACHMENT UNSTABLE SEPARATION: OPPOSING FLOW

70. POTENTIAL FLOW SEPARATION INSTABILITY

71. TROUBLE: TRAILING EDGE
POTENTIAL FLOW SEPARATION:
UNPHYSICAL UNSTABLE: OPPOSING FLOW
POTENTIAL FLOW ATTACHMENT:
PHYSICAL STABLE
NON-POTENTIAL FLOW SEPARATION??
3D ROTATIONAL SEPARATION: PHYSICAL STABLE: AVOIDS OPPOSING FLOW

72. CIRC CYLINDER: POTENTIAL FLOW: P = 0 P = 1 P = - 3 V = 1 V = 0 V = 2 ZERO LIFT DRAG

73. CIRCULAR CYLINDER: 3D ROTATIONAL SEPARATION: LOW MEAN PRESSURE

74. 3D ROTATIONAL SEPARATION

75. KUTTA-ZHUKOVSKY CIRCULATION THEORY VS NEW THEORY

76. STREAMWISE VORTICITY

77. 3D SEPARATION AT TRAILING EDGE
3D ROTATIONAL SEPARATION:
WITHOUT PRESSURE RISE
WITHOUT PRESSURE DROP: WAKE
ELEGANT SEPARATION
PRESSURE RISE:
2D IRROTATIONAL POTEN. FLOW SEPARATION
PRESSURE DROP: WAKE SEPARATION

78. THE SECRET POTENTIAL FLOW: BEFORE SEPARATION
NON-POTENTIAL AT SEPARATION:
3D ROTATIONAL SLIP SEPARATION WITH POINT STAGNATION
256 YEARS: TO UNDERSTAND

79. FROM CYLINDER TO AIRFOIL: ROUNDED LEADING + TRAILING EDGE UNDERST CYL = UNDERSTAND AIRFOIL

80. THE SECRET: L/D = 10

81. THE SECRET INCOMPRESSIBLE SLIGHTLY VISCOUS FLOW
POTENTIAL FLOW BEFORE SEPARATION
3D TRAILING EDGE SEPARATION WITHOUT PRESSURE RISE/DROP

82. SECRET OF FLIGHT HOW TO SEPARATE IN AN ELEGANT WAY:
WITHOUT PRESSURE RISE/DROP
ENGAGEMENT: EASY
DIVORCE: DIFFICULT
THE TRICK: ELEGANT DIVORCE

83. NEW THEORY: NEW WING DESIGN HUMPBACK WHALE LEADING EDGE

84. NEW THEORY: NEW DESIGN ROUNDED TRAILING EDGE WIND TURBIN BLADE

85. THE SECRET OF FLIGHT WEB SITE
FULL STORY
MATHEMATICS
PHYSICS
COMPUTATION
APPLICATIONS: SAILING, SWIMMING,….
BACKGROUND
HISTORY INCORRECT THEORY…